In this paper, we present a path following control law that formally
guarantees practical convergence of magnetic microswimmers to desired straight lines
with absolutely continuous velocity profiles while respecting the
control input saturation limits in the presence of disturbances. Our path following scheme uses an
optimal decision strategy (ODS)-based control synthesis approach. ODS-based
strategies belong to the larger family of optimization-based
nonlinear controllers [1]}, [2]}, [3]}, whose applications in robotics and driverless
cars are growing, thanks in part to recent advancements in mobile computation
power. Optimal decision strategies, which were originally proposed in the context of
controlling electric power systems and industrial robotic manipulators with bounded
input [4]}, [5]}, [6]}, are pointwise optimal control laws
that minimize the deviation between the open-loop dynamics vector field
and a reference model vector field. We propose using
an integral line-of-sight
(ILOS)-based reference vector field for our ODS-based control scheme inspired from the ILOS path following laws that are
widely used for underactuated marine craft control [7]}, [8]}). Our proposed ILOS-based guidance law incorporates the integral of the cross-track error of the
microswimmer to the straight line.
